In the modern information era, a random number plays an important role in various fields such as economy, science, national defense and industry manufacture. Specifically, it has a very important application in various aspects, such as statistic analysis, simulation in the fields of industry and science, cryptology and lottery industry in life. With the classical method, only a pseudo-random number can be generated. The pseudo-random number just seems like the random number, i.e., there is a tiny possibility to distinguish the pseudo-random number and the random number in a limited time under the existing scientific and technical level. However, the entropies thereof are different in nature. So, the pseudo-random number cannot be applied directly in many fields since absolute safety cannot be guaranteed in fields such as safe communication.
According to the randomness of classical physical process, for example the random number may be generated by using noise of an electronic element. Although such random number does not bring risk with the development of computation capacity, the randomness thereof is not guaranteed naturally.
According to the basic principle of quantum mechanics, a quantum random generator may generate a real random number. In the past decades, many solutions for the quantum random generator are proposed, for example a detection using single photon, quantum non-locality and vacuum fluctuation have been successfully experimentally demonstrated. Meanwhile, the commercial quantum random number generator, such as the ID-Quantique system has entered the market. However, it should be noted that, it is unavoidable that these quantum random number generators depends on an assumption of models and a demand on the performance of equipment.
In the numerous quantum random number generators, the one using the single photon detection method is simplest, which mainly includes two parts: source and measure device. In the quantum random number generator using the single photon detection, the source sends a quantum state in Z basis to a detector, and then the detector performs a measurement in an X basis. As described above, according to the basic principle of quantum mechanics, the result obtained by the detector is the real random number. However, if the source does not contain randomness (for example, the source sends an X basis state), the result obtained by the measurement is a constant string without any randomness. Thus, in the quantum random number generator using the single photon detection, the randomness of the source is very important.
However, in the actual application, it is hard to ensure that the source contains enough quantum randomness, such that the resultant random number cannot be guaranteed. At present, a real random number guaranteed by the quantum mechanics is mainly generated by directly using the known source to perform the quantum measurement. Specifically, there are two ways as follows.
Way 1: as described in the white paper of the ID-Quantique random number generator, an LED radiates single photons to a Beamsplitter, and then two single photon detectors detect the photons being transmitted or reflected, respectively. Since it is in nature a quantum effect to transmit or reflect a single photon, the real random number may be obtained.
Way 2: as described in a scientific research paper published by one of the applicants, the phase fluctuation in the laser with low lightness is converted into the light intensity fluctuation by PLC-MZI, and then the light intensity is detected by a light intensity detector and is converted into an 8-bit binary string by using ADC. If the laser is weak enough, there are more phase fluctuations than classic fluctuations for the quantum, such that the real random number may be generated.
In one of the above two ways, an assumption is made about the source. In way 1, it is required to assume that the source is a single photon source. In way 2, it is required to assume that the phase fluctuations of laser are actually about the quantum and more than the classic fluctuations, which may be used as an assumption of source. However, these assumptions of the source cannot be verified in actual applications, such that there may be a big loophole in the randomness of the resultant random number. And even though these assumptions of the source are tenable, it is hard to ensure that the source contains enough quantum randomness in actual applications and the resultant random number cannot be guaranteed.